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## Homework Statement

A 1.2kg mass moving 2.4m/s [East] has an elastic collision with a 2.4kg mass moving 1.8m/s [North]. What are the final velocities?

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I know that I need Ek before and after the collision, but I'm not sure how to calculate it for this scenario (a way that would allow me to substitute into Conservation of Momentum find velocities of both objects). I know it's a scaler quantity, so does that mean I do not have to consider making the energy perpendicular to each other?

## Homework Equations

p = m1v1 + m2v2

Ek = 1/2 mv^2

## The Attempt at a Solution

Here's what I've got so far but I don't know if it's right so I don't want to be doing repeated mistakes throughout my homework and then later on the unit test.

For E-W direction:

p = p'

m1v1 + m2v2 = m1(v1') + m2(v2')

1.2(2.4) + 0 = 1.2(v1') + 2.4(v2')

2.4 = v1' + 2(v2)'

Since it is an elastic collision, I attempted with pure energy since it's scaler, this is what I'm not sure about:

Ek = Ek'

1/2 m(v1)^2 + 1/2 m(v2)^2 = 1/2 m(v1')^2 + 1/2 m(v2')^2

1.2(2.4)^2 + 2.4(1.8)^2 = 1.2(v1')^2 + 2.4(v2')^2

14.688 = 1.2(v1')^2 + 2.4(v2')^2

12.24 = (v1')^2 + 2(v2')^2

12.24 - 2(v2')^2 = (v1')^2

Sqrt {12.24 - 2(v2')^2} = v1'

Then I substituted it into the momentum equation

2.4 = Sqrt {12.24 - 2(v2')^2} +2(v2)'

After squaring both sides and getting the roots of the quadratic equation, I got:

v2' = 2.1 or v2'= -0.51

I reasoned that the ball heading North (v2) should not suddenly start going West when the ball hitting it is heading East.

I end up with final E-W velocities of:

v2' = 2.1m/s [E] and v1' = 1.8m/s [W]

However, these are only Velocities in a East/West direction.

Am I doing this right?

I don't want to do a whole page of calculations for NS direction as well and then make a vector triangle just to find out I did the whole thing wrong.

Thank you for the help!

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